A new approach to solve the inverse scattering problem for waves: combining the TRAC and the adaptive inversion methods

The aim of this paper is to propose a new method to solve the inverse scattering problem. This method works directly in the time-dependent domain, using the wave equation and proceeds in two steps. The first step is the time-reversed absorbing condition (TRAC) method to reconstruct and regularize the signal and to reduce the computational domain. The second step is the adaptive inversion method to solve the inverse problem from the TRAC data, by using basis and mesh adaptation. This strategy allows us to recover the position, the shape and the properties of the scatterer in a precise and robust manner.